lmom.references {lmomco} | R Documentation

## Useful References Related to L-moments

### Description

A subtantial body of statistical research provides foundation for the theory of L-moments and demonstration of L-moment theory in practice exists. Whereas, in many ways, J.R.M. Hosking should be considered the father of L-moments, there are indeed many contributors to L-moment literature. E.A.H. Elamir and A.H. Seheult in 2003 introduced the concept of trimmed L-moments and further, R. Serfling and P. Xiao in 2006 have taken up the reigns of multivariate L-moments. A substantial sampling is provided in the documentation of this package for the benefit of users.

### Author(s)

W.H. Asquith

### References

Asquith, W.H., 1998, Depth-duration frequency of precipitation for Texas: U.S. Geological Survey Water-Resources Investigations Report 98–4044, 107 p.

Asquith, W.H., 2002, Effects of regulation on L-moments of annual peak streamflow in Texas: U.S. Geological Survey Water-Resources Investigations Report 01–4243, 66 p.

Asquith, W.H., 2003, Modeling of runoff-producing rainfall hyetographs in Texas using L-moment statistics: Ph.D. dissertation, University of Texas at Austin, Austin, Texas, 386 p.

Asquith, W.H., and Roussel, 2004, Atlas of depth-duration frequency of precipitation annual maxima for Texas: U.S. Geological Survey Scientific Investigations Report 2004–5041, 106 p.

Cunnane, C., 1989, Statistical distributions for flood frequency analysis: World Meteorological Organization Operational Hydrology Report No. 33, variously paged.

David, H.A., 1981, Order statistics: John Wiley and Sons Inc., New York, 360 p.

Dingman, S.L., 2002, Physical Hydrology: Prentice Hall, New Jersey, 2nd edition, 646 p.

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.

Evans M., Hastings, N.A.J., and Peacock, J. B., 2000, Statistical distributions, 3rd ed.: John Wiley and Sons Inc., 221 p.

Fill, H.D., and Stedinger, J.R., 1995, L-moment and probability plot correlation coefficient goodness-of-fit tests for the Gumbel distribution and impact of autocorrelation: Water Resources Research, vol. 31, no. 1, pp. 225–229.

Gilchrist, W.G., 2000, Statistical modeling with quantile functions: Chapman and Hall CRC Press, Boca Raton, Fla., 320 p.

Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, J.R., 1979, Probability weighted moments-definition and relation to parameters of several distributions expressible in inverse form: Water Resources Research, vol. 15, pp. 1029-1054.

Haktanir, T., and Bozduman, A., 1995, A study on sensitivity of the probability- weighted moments method on the choice of the plotting position formula: Journal of Hydrology, vol. 168, pp. 265–281.

Hosking, J.R.M., 1986, The theory of probability weighted moments, Research Report RC12210, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., 1989, Some theoretical results concerning L-moments, Research Report RC14492, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combination of order statistics: Journal Royal Statistical Society, B, vol. 52, no. 1, pp. 105–124.

Hosking, J.R.M., 1992, Moments or L moments? An example comparing two measures of distributional shape: The American Statistician., vol 46, no. 3, pp. 186-189.

Hosking, J.R.M., 1994, The four-parameter Kappa distribution: IBM Journal of Research and Development, vol. 38, no. 3, pp. 251–258.

Hosking, J.R.M., 1995, The use of L-moments in the analysis of censored data, in Recent Advances in Life-Testing and Reliability, edited by N. Balakrishnan, chapter 29, CRC Press, Boca Raton, Fla., pp. 546–560.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments, version 3: Research Report RC20525, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., and Wallis, J.R., 1987, Parameter and quantile estimation for the generalized Pareto distribution: Technometrics, vol. 29, pp. 339–349.

Hosking, J.R.M., and Wallis, J.R., 1993a, Some statistics useful in regional frequency analysis: Water Resources Research, vol. 29, no. 2, pp. 271–281.

Hosking, J.R.M., and Wallis, J.R., 1993b, Some statistics useful in regional frequency analysis, Research Report RC-17096, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, New York, 23 p.

Hosking, J.R.M., and Wallis, J.R., 1995, A comparison of unbiased and plotting- position estimators of L moments: Water Resources Research, vol. 31, no. 8, pp. 2019–2025.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press, 224 p.

Hosking, J.R.M., Wallis, J.R., and Wood, E.F., 1985, Estimation of the generalized extreme-value distribution by the method of probability-weighted moments: Technometrics, vol. 27, pp. 251–261.

Kaigh, W.D., and Driscoll, M.F., 1987, Numerical and graphical data summary using O-statistics: The American Statistician, vol. 41, no. 1, pp. 25–32.

Karian, Z.A., and Dudewicz, E.J., 2000, Fitting statistical distributions—The generalized lambda distribution and generalized bootstrap methods: CRC Press, Boca Raton, FL, 438 p.

Kirby, W., 1974, Algebraic boundedness of sample statistics: Water Resources Research, vol. 10, pp. 220–222.

Landwehr, J.M., Matalas, N.C., and Wallis, J.R., 1979a, Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles: Water Resources Research, vol. 15, no. 5, pp. 1055–1064.

Landwehr, J.M., Matalas, N.C., and Wallis, J.R., 1979b, Estimation of parameters and quantiles of Wakeby distributions: Water Resources Research, vol. 15, no. 5, pp. 1362–1379.

Schaefer, M.G., 1989, Characteristics of extreme precipitation events in Washington State: Washington State Department of Ecology Report 89–51, variously paged.

Schaefer, M.G., 1993, Dam safety guidelines technical note 3-Design storm construction: Washington State Department of Ecology Report 92–55G, variously paged.

Serfling, R., and Xiao, P., 2006, Multivariate L-moments: preprint

Stedinger, J.R., Vogel, R.M., and Foufoula-Georgiou, E., 1992, Frequency analysis of extreme events, in Handbook of Hydrology, chapter 18, editor-in-chief D. A. Maidment: McGraw-Hill, New York.

Vogel, R.M., and Fennessey, N.M., 1993, L moment diagrams should replace product moment diagrams: Water Resources Research, vol. 29, no. 6, pp. 1745-1752.

Wallis, J.R., Matalas, N.C., and Slack, J.R., 1974, Just a moment!: Water Resources Research, vol. 10, pp. 211–219.

Wang, Q.J., 1996a, Using partial probability weighted moments to fit the extreme value distributions to censored samples: Water Resources Research, vol. 32, no. 6, pp. 1767–1771.

Wang, Q.J., 1996b, Direct sample estimators of L-moments: Water Resources Research, vol. 32, no. 12., pp. 3617–3619.

Zafirakou-Koulouris, A., Vogel, R.M., Craig, S.M., and Habermeier, J., 1998, L-moment diagrams for censored observations: Water Resources Research, vol. 34, no. 5, pp. 1241–1249.

[Package lmomco version 0.92 Index]